Question

Use the shortcut rules to mentally calculate the derivative of the given function. HINT [See Examples 1 and 2.] f(x) = 4x⁴ + 7x³ − 3

f '(x) =

Use the shortcut rules to mentally calculate the derivative of the given function. HINT [See Examples 1 and 2.] f(x) = −x + (8/x) +1

f '(x) =

Find the derivative of the function. HINT [See Examples 1 and 2.] f(x) = 8x³ − 4x² + x

f '(x) =

Find the derivative of the function. HINT [See Examples 1 and 2.] g(x) = x⁻² − 5x⁻¹ − 8

g'(x) =

Find the derivative of the function.h(x) = (8/x² )+ (5/x³ )

h '(x) =

Find the derivative of the function.t(x) = 7|x| + (7/x)

t '(x) =

Find the derivative of the function. HINT [First expand the given function.] s(x) = x(x² −(6/x))

s'(x) =

Evaluate the given expression. (d/dx)[1.1(x − |x|)]

Find the slope of the tangent to the graph of the given function at the indicated point. HINT [Recall that the slope of the tangent to the graph of

f at x = a is f '(a).] f(x) = (x/2) − 1;  (−2, −2)

f '(−2) =

Find the equation of the tangent line to the graph of the given function at the point with the indicated x-coordinate.

f(x) = x³; x = −1

y =

The price per barrel of crude oil in the period 1980–2013, in constant 2014 dollars, can be approximated by P(t) = 0.27t² − 8.6t + 93 dollars (0 ≤ t ≤ 33), where t is time in years since the start of 1980.† Find P'(t) and P'(22).

P'(t)=

P'(22)= $ per year

What does the second answer tell you about the price of crude oil? Hint [See Example 2.]

The price of a barrel of crude oil was increasing at a rate of $ per year in .

Answer 1